Proposed Canon
Thinkagrams are a means of long distance communication between two or more Units. The Spell can be one-way or two-way. The Spell is cast by the Caster, who does not need to be the target. A floating, visual image of the target appears before the recipientErf-b1-p109, allowing other Units in the vicinity to observe the effect. Anything spoken by the target is heard by the recipient and other observers. If the two-way version is cast, an image of the recipient is displayed to the target and anyone observing the casting: anything spoken by the recipient is also heard by the target and observers.
For the duration of the Spell, the fingers of the Caster are held in a rectangle, index fingers to thumbs of opposite handErf-b1-p068, as a Director or Photographer might in a TV show. The image of the recipient appears in front of this rectangle.Erf-b1-p091
Unknown to non-Thinkamancers, (according to LIAB_Text_38) a Thinkagram was not one type of spell. There was a spectrum, from which a Thinkamancer would choose one or more bands to communicate within.